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Wireless mesh network (WMN) has recently emerged as a promising technology for next-generation wireless networking. In WMNs, many important applications, such as mobile TV and video/audio conferencing, require the support of multicast communication with quality-of-service (QoS) guarantee. In this paper, we address the QoS multicast routing issue in WMNs. Specifically, we propose a novel network graph preprocessing approach to enable traffic engineering and enhance the performance of QoS multicast routing algorithms. In this approach, we employ prioritized admission control scheme and develop a utility-constrained optimal priority gain policy. Extensive simulation results show that our approach can significantly improve the performance of QoS multicast routing in WMNs.